Higher order theories for the vibration study of doubly-curved anisotropic shells with a variable thickness and isogeometric mapped geometry

Tornabene, Francesco; Viscoti, Matteo; Dimitri, Rossana; Reddy, J. N.

doi:10.1016/j.compstruct.2021.113829

Cited by 68 publications

(16 citation statements)

References 75 publications

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“…The research lines can be roughly classified into those devoted to the analysis of theoretical aspects [7][8][9][10][11][12], to the formulation of computational methods in discrete [13][14][15][16] and continuum framework [17][18][19][20], as well as to the investigations of experimental evidence [21][22][23][24][25][26][27]. The genesis in conceiving the pantographic sheet can be traced back in the grounding idea of non-local materials, and in particular of second or higher gradient theories [28][29][30][31][32][33][34][35][36][37], in which the constitutive law is a function also of the second or higher gradient of the displacement field. In the same context of non-local formulation, it is worth mentioning the peridynamic approach proposed, among the others, in previous studies [38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Shear rupture mechanism and dissipation phenomena in bias-extension test of pantographic sheets: Numerical modeling and experiments

Ciallella

Pasquali

D’Annibale

et al. 2022

Mathematics and Mechanics of Solids

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In this paper, we show that a two-field model for pantographic sheets generalized to include a more refined description of the deformation of interconnecting pivots and structural dissipation is capable of describing the sheets mechanical behavior for (1) cyclic extension tests in elastic regimes and (2) damage initiation. To this aim, we performed two kinds of experimental tests. In the first ones, we tested, remaining in the elastic regime, pantographic sheets under different cyclic loads. Second, we extended the specimens reaching the first rupture. The numerical model was calibrated in order to predict (1) the observed amplitude and shape of hysteretic cycles and (2) the observed localization of the first rupture. In this framework, (1) a simultaneous rupture of several pivots is observed and theoretically justified, (2) the primary dissipation mechanism and rupture initiation are attributed to pivots’ shear deformation.

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Section: Introductionmentioning

confidence: 99%

Shear rupture mechanism and dissipation phenomena in bias-extension test of pantographic sheets: Numerical modeling and experiments

Ciallella

Pasquali

D’Annibale

et al. 2022

Mathematics and Mechanics of Solids

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“…Rayleigh-Ritz method has been implemented in [13] to study the frequency behavior of skew plate with variable thickness on circular variation in Poisson's ratio and linear variation in temperature. Vibration response of generally curved shell structures to different stacking sequences, material typologies, and boundary conditions has been analysed in [14] by using differential quadrature method. Generalized layer-wise (LW) along with generalized differential quadrature (GDQ) method has been used in [15] to analyze anisotropic double curved shells with an arbitrary shape.…”

Section: Introductionmentioning

confidence: 99%

Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

Sharma

Bhardwaj

Lather

et al. 2022

Mathematical Problems in Engineering

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In this study, two-dimensional circular thickness effects on time period of skew plate made with nonhomogeneous material properties are computed in variable temperature environment. Clamped C , simply supported S , and free-edge F conditions are the various combinations considered in this work. One-dimensional circular density and two-dimensional parabolic temperature variation on the plate are considered due to the nonhomogeneous nature of the material and variable temperature environment. Rayleigh–Ritz method is used to compute the time period for the first two modes of vibration. A convergence study of frequency modes of skew plate on various edge conditions has also been performed. The present work has been compared with the frequency modes of parallelogram and rectangle plate on various edge conditions. The objective of the study is to present a numerical data of time period as well as to show how one can control the frequencies of plate by taking an appropriate variation in plate parameters.

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“…Huang JL 10 proposed a new incremental harmonic balance method to study the quasi periodic motion of an axially moving beam, which is verified the effectiveness by comparing the frequency and amplitude. Tornabene F 11 established the governing equation of the thin shell by using Hamilton’s principle and get it solved by using the generalized differential quadrature method. MH Ghayesh 12 obtained the nonlinear dynamic equation of the forced motion of the axially moving plate based on the energy method.…”

Section: Introductionmentioning

confidence: 99%

Study on nonlinear vibration of flexible electronic membrane engendered by high-precision imprinting system

Feng

Wang

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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In the process of guide roller transmission, the geometric nonlinearity caused by the lateral vibration of the flexible electronic membrane will result in the divergence and instability of the membrane velocity, thus affecting the printing accuracy. In this paper, in order to engineer the exact condition that affecting the printing accurancy, the Elliptic integral method, whose effectiveness has been verified for its soluted result, is consistent with the one concluded from L-P method and He's Frequency formula while soluting the nonlinear vibration equation, respectively, on basis of Von Karman’s large deflection theory and Hamilton’s principle, is mainly applied, and thus provide a theoretical support for the design and manufacture of high-precision flexible electronic printing press.

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Higher order theories for the vibration study of doubly-curved anisotropic shells with a variable thickness and isogeometric mapped geometry

Cited by 68 publications

References 75 publications

Shear rupture mechanism and dissipation phenomena in bias-extension test of pantographic sheets: Numerical modeling and experiments

Shear rupture mechanism and dissipation phenomena in bias-extension test of pantographic sheets: Numerical modeling and experiments

Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

Study on nonlinear vibration of flexible electronic membrane engendered by high-precision imprinting system

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